A weak type estimate for oscillatory singular integrals

The Ricci-Stein theory of singular integrals concerns operators of the form \int e^{i P(y)} f (x-y) \frac {dy}y.The L^p boundedness was established in the early 1980's, and the
weak-type L^1 estimate by Chanillo-Christ in 1987. We establish the
weak type estimate for the maximal truncations. This method of proof
might well shed much more information about the fine behavior of these
transforms. Joint work with Ben Krause.